<header>
    求导法则
</header>
<p>
    <span class="title">
        定理
    </span>
    若函数u(x)和v(x)在点x<sub>0</sub>可导，则函数ƒ(x)=u(x)±v(x)在点x<sub>0</sub>也可导，且
    <span class="oneline">
        ƒ<sup>'</sup>(x<sub>0</sub>)=u<sup>'</sup>(x<sub>0</sub>)±v<sup>'</sup>(x<sub>0</sub>)
    </span>
</p>
<p>
    <span class="title">
        定理
    </span>
    若函数u(x)和v(x)在点x<sub>0</sub>可导，则函数ƒ(x)=u(x)v(x)在点x<sub>0</sub>也可导，且
    <span class="oneline">
        ƒ<sup>'</sup>(x<sub>0</sub>)=u<sup>'</sup>(x<sub>0</sub>)v(x<sub>0)</sub>+u(x<sub>0</sub>)v<sup>'</sup>(x<sub>0</sub>)
    </span>
</p>
<p>
    <span class="title">
        定理
    </span>
    若函数u(x)和v(x)在点x<sub>0</sub>都可导，且v(x<sub>0)</sub>≠0，则函数ƒ(x)=
    <code>
        ["division","u(x)","v(x)"]
    </code>
    在点x<sub>0</sub>也可导，且
    <span class="oneline">
        ƒ<sup>'</sup>(x<sub>0</sub>)=
        <code>
            ["division",
            ["join",["rightTop","u","'"],"(",["rightBottom","x","0"],")","v(",["rightBottom","x","0"],") - u(",["rightBottom","x","0"],")",["rightTop","v","'"],"(",["rightBottom","x","0"],")"],
            ["rightTop",["bracket",["join","v(",["rightBottom","x","0"],")"],"middle"],"2"]]
        </code>
    </span>
</p>
<h2>
    基本初等函数导数公式
</h2>
<ol>
    <li>
        (c)<sup>'</sup>=0 (c为常数)
    </li>
    <li>
        (x<sup>α</sup>)<sup>'</sup>=αx<sup>α-1</sup> (α为任意常数)
    </li>
    <li>
        (sinx)<sup>'</sup>=cos , (cosx)<sup>'</sup>=-sinx , (tanx)<sup>'</sup>=sec<sup>2</sup>x ,
        (cotx)<sup>'</sup>=-csc<sup>2</sup>x , (secx)<sup>'</sup>=secxtanx , (cscx)<sup>'</sup>=-cscxcotx
    </li>
    <li>
        (arcsinx)<sup>'</sup>=<code>["division","1",["gen",["join","1 -",["rightTop","x","2"]]]]</code> ,
        (arccosx)<sup>'</sup>= -<code>["division","1",["gen",["join","1 -",["rightTop","x","2"]]]]</code> ,
        (arctanx)<sup>'</sup>=<code>["division","1",["join","1 +",["rightTop","x","2"]]]</code> ,
        (arccotx)<sup>'</sup>= -<code>["division","1",["join","1 +",["rightTop","x","2"]]]</code>
    </li>
    <li>
        (a<sup>x</sup>)<sup>'</sup>=a<sup>x</sup>lna , (e<sup>x</sup>)<sup>'</sup>=e<sup>x</sup>
    </li>
    <li>
        (log<sub>a</sub>x)<sup>'</sup>=<code>["division","1","xlna"]</code> ,
        (lnx)<sup>'</sup>=<code>["division","1","x"]</code>
    </li>
</ol>